Question

find the missing side. round to the nearest tenth.
1)
2)
3)
4)
5)
6)
7)
8)

Explanation:

Step1: Recall the cosine formula

For a right - triangle, $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$

Problem 1

• $\cos72^{\circ}=\frac{6}{x}$
• $x = \frac{6}{\cos72^{\circ}}$
• $\cos72^{\circ}\approx0.3090$
• $x=\frac{6}{0.3090}\approx19.4$

Problem 2

• $\cos73^{\circ}=\frac{x}{6}$
• $x = 6\times\cos73^{\circ}$
• $\cos73^{\circ}\approx0.2924$
• $x = 6\times0.2924\approx1.8$

Problem 3

• $\tan24^{\circ}=\frac{x}{12}$
• $x = 12\times\tan24^{\circ}$
• $\tan24^{\circ}\approx0.4452$
• $x = 12\times0.4452\approx5.3$

Problem 4

• $\tan37^{\circ}=\frac{x}{12}$
• $\tan37^{\circ}\approx0.7536$
• $x = 12\times0.7536\approx9.0$

Problem 5

• $\tan49^{\circ}=\frac{14}{x}$
• $x=\frac{14}{\tan49^{\circ}}$
• $\tan49^{\circ}\approx1.1504$
• $x=\frac{14}{1.1504}\approx12.2$

Problem 6

• $\cos51^{\circ}=\frac{14}{x}$
• $x=\frac{14}{\cos51^{\circ}}$
• $\cos51^{\circ}\approx0.6293$
• $x=\frac{14}{0.6293}\approx22.2$

Problem 7

• $\cos63^{\circ}=\frac{16}{x}$
• $x=\frac{16}{\cos63^{\circ}}$
• $\cos63^{\circ}\approx0.4540$
• $x=\frac{16}{0.4540}\approx35.2$

Problem 8

• $\sin15^{\circ}=\frac{16}{x}$
• $x=\frac{16}{\sin15^{\circ}}$
• $\sin15^{\circ}\approx0.2588$
• $x=\frac{16}{0.2588}\approx62.6$

Answer:

1. $19.4$
2. $1.8$
3. $5.3$
4. $9.0$
5. $12.2$
6. $22.2$
7. $35.2$
8. $62.6$